I have elsewhere argued (Ariel, 2002) against the assumption that we can identify one literal meaning per sentence. Instead, I have suggested that there are (at least) three types of minimal meanings, each differently motivated. One implicit motivation behind the classical definition of literal meaning (Grice's 'what is said') is a wish to capture the core content of sentences. I here examine discourse in order to characterize this type of minimal meaning, which I term 'privileged interactional interpretation'. Privileged interactional interpretations constitute what the speaker is taken to be truthfully or sincerely committed to. Crucially, they also constitute the speaker's relevant contribution to the discourse. I argue that Sperber and Wilson's (1986b/1995) explicatures (linguistic meanings enriched up to full propositionality) are commonly perceived as privileged interactional interpretations, but not invariably so. Interlocutors pick both less enriched meanings (enriched but incomplete propositions, irrelevant unenriched linguistic meanings) and more enriched meanings (particularized and generalized conversational implicatures) as their privileged interactional interpretations. Thus, no single formula of meaning representation (be it linguistic meaning, 'what is said', explicature, implicature, conveyed meaning) can define a privileged interactional interpretation appropriate for all occasions. (C) 2002 Elsevier Science B.V. All rights reserved.